Question

If $12$ represents the area of a rectangle, then in how many different ways this rectangle can be drawn so that measures of its sides are natural numbers?

Answer 1

Different ways of measuring rectangle whose area is $12$ and sides natural number are all possible factors of $12$.

Different possible factor of $12$ are

$$\begin{gathered} 12=1\times 12 \\ 12=2\times 6 \\ 12=3\times 4 \end{gathered}$$

As we can see $12$ can be multiple of $(1,12),(2,6)and(3,4)$.

Hence, $3$ different ways this rectangle can be drawn so that measures of its sides are natural numbers.